Question

a triangle has side lengths of (9.9c + 5.1d) centimeters, (6.2c + 1.6f) centimeters, and (2.5f + 6.2d) centimeters. which expression represents the perimeter, in centimeters, of the triangle? answer 8.7df + 7.8cf + 15cd 18.6cf + 12.9df 4.1f + 11.3d + 16.1c 8.7f + 6.7d + 16.1c

Explanation:

Step1: Recall perimeter formula

The perimeter \(P\) of a triangle is the sum of the lengths of its sides. So \(P=(9.9c + 5.1d)+(6.2c + 1.6f)+(2.5f + 6.2d)\).

Step2: Combine like - terms for \(c\)

Combine the \(c\) terms: \(9.9c+6.2c=(9.9 + 6.2)c = 16.1c\).

Step3: Combine like - terms for \(d\)

Combine the \(d\) terms: \(5.1d+6.2d=(5.1 + 6.2)d=11.3d\).

Step4: Combine like - terms for \(f\)

Combine the \(f\) terms: \(1.6f+2.5f=(1.6 + 2.5)f = 4.1f\).

Step5: Write the perimeter expression

The perimeter \(P = 4.1f+11.3d + 16.1c\).

Answer:

\(4.1f + 11.3d+16.1c\)